论文标题
当地时代和田中 - càdlàg路径的梅尔公式
Local times and Tanaka--Meyer formulae for càdlàg paths
论文作者
论文摘要
开发了确定性c {à} dl {à} g路径的三个局部时间概念，并提供了相应的路径田中 - 麦内尔公式。对于半明星，这表明其样品路径A.S.满足当地时代的所有三个路线定义，并且都与经典的半明星当地时间一致。特别是，这表明每个定义构成了概率局部时间的合法路线对应物。本文中提出的最后一个路径构造以归一量的间隔交叉数来表达当地时代，并且不取决于网格序列的选择。对于c {à} dl {à} g semimartingales来说，这也是一个新结果，这可能与妮可·埃尔（Nicole El〜Karoui）和马克·莱米（Marc Lemieux）的先前结果有关。
Three concepts of local times for deterministic c{à}dl{à}g paths are developed and the corresponding pathwise Tanaka--Meyer formulae are provided. For semimartingales, it is shown that their sample paths a.s. satisfy all three pathwise definitions of local times and that all coincide with the classical semimartingale local time. In particular, this demonstrates that each definition constitutes a legit pathwise counterpart of probabilistic local times. The last pathwise construction presented in the paper expresses local times in terms of normalized numbers of interval crossings and does not depend on the choice of the sequence of grids. This is a new result also for c{à}dl{à}g semimartingales, which may be related to previous results of Nicole El~Karoui and Marc Lemieux.
